2004-05 MODEL PAPER

MCA 2.2.3

OPERATIONS RESEARCH

First Question is Compulsory

Answer any four from the remaining

Answer all parts of any Question at one place.

Time: 3 Hrs.
Max. Marks: 100

1. Write short notes on the following:
a) Graphical Method for solving a Linear Programming Problem.
b) Explain the Duality in linear programming.
c) Zero sum Game.
d) Economic order Quantity (EOQ).
e) Min-Max Method.

2. a) Explain the characteristics of LP model.

b) Solve the following LP problem by using Simplex method:
Minimize : z = 2x₁ + 4x₂ + x₃
Subject to 4x₁ + 8x₂ + 2x₃ = 40
-3x₁+2x₂ ≤ 6
x+2x+x=24
x₁, x₂, x₃ = 0

3. a) Explain the reasons for analysing a primal linear programming problem in terms of dual form.

b) Given the following linear programming problem:
Minimize z = 4x₁ + 3x₂
Subject to :
2x₁ + x₂ = 10
-3x₁ + 2x₂ = 6
x₁ + x₂ = 6
x₁ , x₂ = 0
Solve using the dual simplex method.

4. a) Explain the Transportation and Transhipment problems.
b) Given the following Transportation problem:

Find the initial solution by VAM method and optimum solution by MODI method.

5. a) Explain the Travelling Salesman Problem

b) A dispatcher presently has six taxicabs at different locations and five customers who have call for service. The mileage from each taxi’s present location to each curstomer is

Determine the optional assignment that will minimize the total mileage.

6. a) Explain the Critical Path method.
b) A project being planned involved the following activities:

Construct the network.
Determine expected project completion time.
Determine free slack and total slack.

7. a) Explain the Graphical Method for solving a Game.

b) Find the Optimal solution for the following game using Graphical method:

			Player B
		1   2   3   4   5

Player A     4   2   5   -6   6
		7  -9   7   4    8

8. a) Explain the Integer Programming problem.

b) Explain the Branch and Bound Technique for solving an Integer Programming Problem